As for the title:Amplitude of Transmitted Wave in a Two-Part String

In summary, a string with two parts, one with high mass density and one with low mass density, will have a transmitted wave with a different amplitude depending on the densities of the strings. There will be transmission and reflection of energy, and the exact ratio can be found by solving a double wave equation system with a boundary condition. However, for the limiting case where the density ratio is infinite, the amplitude may not change but the frequency between the two parts will. This is not a Quantum Mechanics problem and can be solved by finding a solution in most Partial Differential Equation texts.
  • #1
salsero
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A string has two parts: one with a very high mass density (per unit length), and the other with a very low mass density. A wave with amplitude A moves from the dense part toward the light part. What will be the amplitude of the wave which is transmitted to the light part?
 
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  • #2
This will depend on the different densities of the strings. There will be some transmission and some reflected energy. To get the exact ratio it would be necessary to solve a double wave equation system. with a boundry condition at connection point be that their displacement be the same for all time.

This problem may be solved is some textbooks. If you have access to a university liberary you may want to search the Partial Differential Equation text for a solution.
 
  • #3
I am interested in the limit where the ratio of the densities of the heavy part and the light part is very large (infinite).

Probably the answer to this limiting case can be found without solving differential equations...
 
  • #4
I may be wrong but I don't think the amplitude will change, but the frequency between the two part will. Isn't energy a product of frequency? E=hv
 
  • #5
Originally posted by birdus
I may be wrong but I don't think the amplitude will change, but the frequency between the two part will. Isn't energy a product of frequency? E=hv

This is not a Quantum Mechanics problem, hν has nothing to do with it.

In the limit you speak of the result would be the same as a wave equation with a free end boundry condtion. This should be a easy solution to find in most PDE texts.
 

1. What is a wave in a two-part string?

A wave in a two-part string is a type of mechanical wave that travels through a medium made up of two connected strings. It is characterized by a disturbance that travels through the strings, causing the particles of the medium to vibrate.

2. How is a wave created in a two-part string?

A wave in a two-part string is created by a source of energy, such as a hand or a plucked string, which causes a disturbance in one of the strings. This disturbance then travels through the strings, creating a wave.

3. What factors affect the speed of a wave in a two-part string?

The speed of a wave in a two-part string is affected by the tension of the strings, the mass of the strings, and the length of the strings. In general, higher tension, lower mass, and shorter length will result in a faster wave speed.

4. What happens when a wave reaches the end of a two-part string?

When a wave reaches the end of a two-part string, it can either be reflected or transmitted. If the end of the string is fixed, the wave will be reflected back in the opposite direction. If the end of the string is free to move, the wave will be transmitted to the other string.

5. How does the amplitude of a wave change in a two-part string?

The amplitude of a wave in a two-part string will decrease as the wave travels through the strings due to energy being transferred to the particles of the medium. This is known as wave attenuation. Additionally, the amplitude can be changed by altering the tension, mass, or length of the strings.

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